Small area variations in low birth weight and small size of births in India

Abstract The states and districts are the primary focal points for policy formulation and programme intervention in India. The within‐districts variation of key health indicators is not well understood and consequently underemphasised. This study aims to partition geographic variation in low birthweight (LBW) and small birth size (SBS) in India and geovisualize the distribution of small area estimates. Applying a four‐level logistic regression model to the latest round of the National Family Health Survey (2015–2016) covering 640 districts within 36 states and union territories of India, the variance partitioning coefficient and precision‐weighted prevalence of LBW (<2.5 kg) and SBS (mother's self‐report) were estimated. For each outcome, the spatial distribution by districts of mean prevalence and small area variation (as measured by standard deviation) and the correlation between them were computed. Of the total valid sample, 17.6% (out of 193,345 children) had LBW and 12.4% (out of 253,213 children) had SBS. The small areas contributed the highest share of total geographic variance in LBW (52%) and SBS (78%). The variance of LBW attributed to small areas was unevenly distributed across the regions of India. While a strong correlation between district‐wide percent and within‐district standard deviation was identified in both LBW (r = 0.88) and SBS (r = 0.87), they were not necessarily concentrated in the aspirational districts. We find the necessity of precise policy attention specifically to the small areas in the districts of India with a high prevalence of LBW and SBS in programme formulation and intervention that may be beneficial to improve childbirth outcomes.


| INTRODUCTION
Many studies estimated the district-level prevalence of health indicators in India (International Institute for Population Sciences [IIPS] and ICF, 2017; Menon et al., 2018).
The practice of estimating health indicators at the district level may mask inequalities between small areas, such as administrative blocks and villages within districts. Adopting a multilevel approach, recent studies have identified substantial small area variation within the district in a range of development and health indicators, such as body mass index (BMI) for women, poverty, child sex ratio and child nutrition (Kim et al., 2016Mohanty et al., 2018;Rajpal et al., 2021;Rodgers et al., 2019). These findings support the supposition that there are small area inequalities within a relatively larger area like a district. For example, it was found that districts in India with a higher average prevalence of child undernutrition also have a higher level of inequalities within them (Rajpal et al., 2021).
Low birth weight (LBW) is an important indicator of the health of the mother and her children, and of the quality of maternal health care. It is a single measure that captures intrauterine growth influenced by several causes, from distal such as socioeconomic, environmental factors to proximal factors, such as maternal undernutrition, infections and clinical status (World Health Organisation [WHO], 2022). LBW increases the likelihood of several health complications, such as malnutrition, neurological disorders, respiratory suffering, hypoglycaemia and perinatal asphyxia (De Kieviet et al., 2009;Delobel-Ayoub et al., 2006;Kramer, 1987;Marlow et al., 2005;Van Baar et al., 2005). It also increases the risk of lifelong illness and developmental disabilities, including diabetes, coronary heart diseases, high blood pressure, emotional distress and disabilities related to the physique, nervous system and intellect (Conde-Agudelo et al., 2000;Wilson-Costello et al., 2005).
Prior studies have identified a range of socioeconomic and demographic characteristics, such as caste groups, wealth status, use of maternity care and maternal nutritional status, in relation to increased risk of LBW in India (Bharati et al., 2011;Chakraborty & Anderson, 2011;Deshpande Jayant et al., 2011;Dharmalingam et al., 2010; International Institute for Population Sciences [IIPS] and ICF, 2017;Islam & Mohanty, 2021;Kader & Perera, 2014;Khan et al., 2020). Geographical factors can also help explain the withincountry differences in the prevalence of LBW (Yadav et al., 2015).
Given the diversity of population characteristics and regional differences in India, it is highly likely that adverse birth outcomes like LBW will exhibit substantial geographic variation. While previous studies have mostly focused on the associations between socioeconomic and health factors with the risk of LBW, the analyses of geographical variance and small area variation have not been adequately considered in the previous studies (Balarajan et al., 2013;Banerjee et al., 2020;Bharati et al., 2011;Chakraborty & Anderson, 2011;Deshpande Jayant et al., 2011;Dharmalingam et al., 2010;Islam & Mohanty, 2021;Kader & Perera, 2014;Khan et al., 2020;Muthayya, 2009;Sen et al., 2010).
Assessment of small area variation is needed to identify districts that have not only higher prevalence but also larger within-district disparity.
This identification of high burdened small areas within districts can help the policy makers and programme implementers to set priorities for effective policy intervention.

Key messages
• The small areas contribute the highest share of the total geographic variance of low birth weight (LBW) and small birth size (SBS) in India.
• A high burden of LBW is found mostly in the centralwestern part of India and Odisha. The prevalence of SBS is high across the district of northern-western regions and the north-eastern regions of India.
• The mean prevalence and standard deviation are strongly correlated in the case of both LBW (r = 0.88) and SBS (r = 0.87) in India. It indicates that the districts which have a higher prevalence of LBW and SBS also have a higher between small area disparity within the districts.
• We find a similar pattern of distribution in LBW and SBS between the policy-focused aspirational districts and other districts of India.
• Findings indicate reprioritizing the policy intervention, focusing on the small areas of India for better childbirth outcomes.
weight is relatively higher. So, there is a need to carry out a separate exercise for SBS in addition to the LBW.
The present study aims to estimate the multilevel geographical variance, precision-weighted prevalence and small area variation of LBW and SBS in India. There are four specific objectives: (1) to partition the total geographic variation and estimate how much is attributable to the states, districts and small areas, (2) to assess the regional heterogeneity in the geographic variance explained by small areas across states and union territories, (3) to present the precisionweighted prevalence and small area variation of LBW and SBS across the districts of India, and its correlation to variance across districts, and (4) to identify the policy-prioritised districts in India based on the prevalence and small area variation.
2 | DATA AND METHODS

| Survey data and study population
Our data has been drawn from the National Family Health Survey completed the interviews with a response rate of 97%. Among the women interviewed, a total of 259,469 babies were born in the 5 years preceding the survey. After excluding the babies who were not weighed at the time of birth, as well as those whose birth weight information was not available at the time of the survey, 193,345 participants were included in the analysis of LBW. Similarly, a total of 253,213 births were included in the analyses of SBS after removing the cases whose birth sizes were 'missing/don't know' (Figure 1).

| Study design
This cross-sectional survey used a two-stage stratified random sampling framework. In the first stage, the primary sampling units Schematic of the participantselection procedure with the hierarchy of sample distribution for birth weight and birth size in India, NFHS-4 (2015-2016) per female literacy. The population proportion to size (PPS) sampling method was applied for selecting the small areas for sampling. If the number of households in the selected small areas was at least 300, the small areas were segmented into blocks with 100-150 households. Two of these segments were then selected for the sampling. In the second stage, a fixed number of 22 households were selected using systematic random sampling from each chosen small area.

| Variables of interest
The main variables of interest in this study were LBW and SBS. The For SBS, a question was posed to the mothers during the survey: When (NAME) was born, was (he/she) very large, larger than average, average, smaller than average or very small? From their responses, the variable of SBS was created. The SBS was defined as children who were reported as 'very small' or 'smaller than average' at the time of birth (coded as 1). The children who were reported as 'average', 'larger than average' or 'large' were categorised as normal (coded as 0). To understand the severity of SBS, a secondary variable of very small birth size (VSBS) was also created and categorised into two groups-namely, VSBS, that is, 'very small' (coded as 1) and normal birth size comprising the respondents of 'smaller than average', 'average', 'larger than average' and 'large' (coded as 0).

| Statistical analyses
Four-level logistic regression models were applied for partitioning the variance in LBW and SBS across the different levels. The levels of variance were children at level-1 (i), small areas at level-2 (j), districts at level-3 (k) and states or union territories at level-4 (l). Thus, the probability of LBW at these four levels can be predicted as: 0 . In this model, β 0 is the constant and c jkl 0 , d kl 0 and s l 0 are the residuals at the small area, district and state levels, respectively. The residuals are assumed to be normally distributed with mean 0 and variance of σ c0 2 , σ d0 2 and σ s0 2 . These variances estimate between small areas within a district (σ c0 2 ), between districts within a state (σ d0 2 ) and between states within the country (σ s0 2 ), respectively. A fixed individual-level variance of π /3 2 or 3.29 can be assumed due to the logistic distribution of the outcome variable (Browne et al., 2005). The multilevel model was applied using the The precision-weighted prevalence of LBW and SBS at the level of small areas were generated from the above-described four-level logistic regression models. In this process, the strengths of a higher sample size at the larger geographical levels (district and states) were borrowed for computing the precision-weighted estimates to make them more reliable (Arcaya et al., 2012;Bell et al., 2019;Goldstein, 2011;Jones & Bullen, 1994;Leckie & Charlton, 2013;Subramanian et al., 2003). The

| Study participants and outcomes
In the selected study population, the prevalence of LBW is around 18% in India (Supporting Information: Table S1). The prevalence of VLBW and ELBW are <2% and <1%, respectively. About 12% and 3% of all children were reported as SBS and VSBS, respectively.
The information on LBW is derived from two sources (namely records from cards and mother's recall), while the information on SBS is the perception of mothers about the size of their children at birth. A sensitivity between LBW and SBS was 38%, with an ROC area of 61% showing a moderate correlation in reporting of SBS and LBW in India at the individual level. The district-level correlation between LBW and SBS also showed a moderate association (r = 0.31) (Supporting Information: Figure S1).

| Relative importance of multilevel geographies
The variance partitioning from the four-level logistic regression models shows that the largest share of geographical variance in both LBW and SBS are attributed to the small areas ( Figure 2). Of the total geographical variance of LBW, the small area shares the largest variance of 53%

| Precision-weighted estimates and small area variation
The district-level prevalence and within-district, between-small areas standard deviation (SD) were computed using the precision-weighted estimates. The spatial distribution of the prevalence and small area variation (as measured by SD) across the districts are presented below (Figure 4), showing that there is a significant variation in the prevalence and SD of LBW across the districts and states of India.
The prevalence of LBW ranges from <11% in the first decile to >22% in the last decile. A high burden of LBW (>16.2%) is found mostly in the central-western part of India (Uttarakhand, Western Uttar Pradesh, part of Madhya Pradesh, Rajasthan, Gujarat and Maharashtra) and Odisha. The SD of LBW is also high in the districts of similar regions. Along similar lines, we found that the districts with a higher prevalence of SBS also had a higher within district SD.

| Correlation between prevalence and small area variation
The position of districts in relation to the district level prevalence and within-district, between small area variation (SD), helps identify those districts that have a different level of prevalence with higher inequality in terms of LBW and SBS. Their relative positions reveal a strong association between prevalence and SD (r = 0.88) for LBW ( Figure 5a). Importantly, the distribution of aspirational districts (in red) in terms of prevalence and SD is very similar to the nonaspirational districts (in green). Across the states and union territories of India, the correlation coefficients between prevalence and SD of the precision-weighted percentage of LBW are significantly high with little variation, from the lowest in Maharashtra (r = 0.62) to the highest in Mizoram and Sikkim (r = 0.98) (Supporting Information: Table S3). The nonexistence of a negative correlation coefficient indicates that there are no states, which have low prevalence with high SD. Similarly, a strong correlation between prevalence and SD in SBS was found ( Figure 5b).

| Identification of policy focused districts
The total number of districts (640)   F I G U R E 3 Geographic variance of (a) low birth weight and (b) small birth size attributable to the small areas (%) across the states and union territories of India, NFHS-4 (2015NFHS-4 ( -2016. Geographic variance for India includes the variance across the states, districts and small areas. Three union territories of India (Chandigarh, Lakshadweep and Dadra and Nagar Haveli) have only one district. Therefore, the geographic variance attributable to small areas is 100% F I G U R E 4 Geographic distribution of (a) prevalence of low birth weight (%), (b) within-district, between-small area standard deviation of low birth weight, (c) prevalence of small birth size (%) and (d) within-district, between-small area standard deviation of small birth size across 640 districts of India, NFHS-4 (2015NFHS-4 ( -2016 factoring small areas into the planning and intervention would accelerate progress towards achieving better birth outcomes. It is important to note that the geographic variance attributed to small areas also varied substantially across the states and union territories of India, indicating that this spatial heterogeneity needs to be considered when within-district small areas are being prioritised.
Currently, the decisions for resource allocation are made targeting the deprived districts. Within the district, small area variation in any diseases is not considered. Given the high concentration of LBW and SBS in select districts and its strong association with the small areas within districts, funding should be assigned contemplating the small area variation within the district.
There are substantial regional differentials in within-district small area variation of LBW and SBS across the districts and states of India, which function as the main hindrance to equitable development.
Well-designed interventions in districts of high small area variation (inequality) would not only help lagging small areas improve but could also accelerate the overall progress of the district in the birth outcomes. Better understanding of these state-wise differences in small area variation would help local governments more precisely prioritise their policy agenda. Since public health is a state concern as per the Seventh Schedule of the Constitution of India, state governments have a major role in framing new programmes and modifying existing ones.
The strong positive correlation between prevalence and SD of LBW and SBS across the districts of India demonstrates that districts with a higher level of prevalence also have higher within-district, between-small areas inequalities. A separate study finds similar patterns of distribution in child anthropometric failures (stunting, underweight and wasting) across the districts of India (Rajpal et al., 2021). Districts that have a low prevalence with high inequality would have critical policy challenges addressing within-district small area variation. Although the number of districts showing low prevalence with high inequality is negligible, a significant number of districts with medium prevalence and high inequality were identified in the policy-focused areas. Instances of high prevalence and high inequality are also key areas of policy concern.
The distribution of prevalence and SD of LBW and SBS across the aspirational districts is not different from that of the nonaspirational districts, implying that the problem of LBW and SBS prevails more uniformly across all districts than assumed in the programme.
As India's aspirational district programme aims to accelerate key health indicators in underperforming districts, the current focus is on these target districts. However, our findings suggest the need for redefining the universe of aspirational districts. To that end, we have identified policy-focused districts with different degrees of priority, factoring in the prevalence and small area variation for the indicators of adverse birth outcomes (Supporting Information: Table S5).

| LIMITATIONS
This study had some limitations. Because about one-fourth of the participants (25.4%) were excluded due to either nonmeasurement of weight at birth or reporting as 'don't know', the unequal distribution of excluded participants across the states and union territories may affect the estimates (Supporting Information: Figure S2). Around half of the excluded samples were from Uttar Pradesh and Bihar. Thus, the estimates in these states may be disproportionately affected. Additionally, in the analyses of LBW, 403 small areas were excluded due to 100% of their cases being reported as missing. The education level and wealth status of respondents from these excluded small areas are significantly lower as compared to the respondents from the included small areas (Supporting Information: Table S6). Therefore, this exclusion of sample and small areas may slightly underestimate the prevalence of LBW in the larger administrative units (districts). Besides these excluded F I G U R E 5 Correlation between the district level percent and within-district, between-small areas standard deviation of children of (a) low birth weight (LBW) and (b) small birth size (SBS) in India, NFHS-4 (2015-16) small areas, the sample size for some of the remaining small areas may also be reduced due to missing cases. In such small areas, the prevalence of LBW may be conservative and skewed towards the district and state mean prevalence. About half of the valid sample (47%) for birth weight was based upon mothers' recall and therefore subject to their recall bias towards digit preference in reporting. The digit preference emerges when mothers tend to report birth weight in certain digits (

CONFLICTS OF INTEREST
The authors declare no conflicts of interest.

DATA AVAILABILITY STATEMENT
DHS data are available at https://dhsprogram.com.

ETHICS STATEMENT
This project used publicly accessible secondary data obtained from the DHS website. The DHS data are not collected specifically for this study and no one on the study team has access to identifiers linked to the data. These activities do not meet the regulatory definition of